TY - UNPB
T1 - The 2-divisibility of divisors on K3 surfaces in characteristic 2
AU - Katsura, Toshiyuki
AU - Kondō, Shigeyuki
AU - Schütt, Matthias
N1 - 28 pages
PY - 2024/10/17
Y1 - 2024/10/17
N2 - We show that K3 surfaces in characteristic 2 can admit sets of $n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each $n=8,12,16,20$. More precisely, all values occur on supersingular K3 surfaces, with exceptions only at Artin invariants 1 and 10, while on K3 surfaces of finite height, only $n=8$ is possible.
AB - We show that K3 surfaces in characteristic 2 can admit sets of $n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each $n=8,12,16,20$. More precisely, all values occur on supersingular K3 surfaces, with exceptions only at Artin invariants 1 and 10, while on K3 surfaces of finite height, only $n=8$ is possible.
KW - math.AG
KW - cs.CR
KW - 14J28 (Primary), 14C20, 14J27 (Secondary)
U2 - 10.48550/arXiv.2410.14085
DO - 10.48550/arXiv.2410.14085
M3 - Preprint
BT - The 2-divisibility of divisors on K3 surfaces in characteristic 2
ER -